The U.S. Pavilion at the 1970 Japan Exposition in Osaka was designed and fabricated as an air-supported glass fiber reinforced membrane structure. Designer interest considered to have been generated as a consequence of this structure has led to the application of air-supported envelopes as roof coverings over the broad expanses, for example, of stadiums and similar arenas. Such roof structures generally are configured as a continuous fabric formed of a resin coated glass fiber material which extends over the arena from a continuous, substantially air secure attachment to a correspondingly continuous compression ring or equivalent supporting structure. This latter compression ring is supported about the top of the peripheral walls of the stadium being enclosed. To restrain the roof web in its designed geometric configuration, a cable system is employed wherein a series of cables extend across the expanse to be covered between predetermined points located upon the compression ring. Several approaches to the structural optimization of the geometric pattern defined by these cables have been developed. See for example, a "skewed symmetry" approach by Geiger, U.S. Pat. No. 3,835,599; or the design of Bird, U.S. Pat. No. 3,744,191.
During erection of the roof structure, the cables are coupled to pivotal connectors structurally attached to the compression ring. Upon essential completion of cable erection, panels of the somewhat flexible glass fiber roof membrane are connected to the compression ring and cables utilizing air secure clamps or the like. During this procedure, the assembly is "down," the cables hanging across the arena in catenary fashion. Upon completion of fabric attachment, a plurality of fans installed within the thus enclosed building are activated to build up the air pressure to predetermined levels depending upon ambient environmental conditions, as well as the design strength of portals and windows within the building structure. As these pressures develop the roof structure is raised to its operational orientation.
An appreciation of the material stress factors enncountered in the design of the air-supported roof structures may be gleaned merely in considering the sizes and weight scales involved in typical installations. For example, the Pontiac Metropolitan Stadium, Pontiac, Mich. is roofed by a cable restrained air-supported roof spanning 722 feet (220 m). Together with the compression ring, the roof cavern of that arena covers ten acres, incorporating eighteen 3-inch diameter cables, the longest of which is 747 feet (227.7 m) in length and weighs 16,000 pounds (7 Mg.). Upon inflation, the rise at the center of the roof is 50 feet.
The structural design approach to such roofs necessarily must look to an avoidance of the development of stress gradients, i.e. stress concentrations at various regions of the fabric and cable structure. In the past, such stress anomalies have been witnessed particularly at those points about the compression ring where both a cable end is coupled and the roof membrane is continuously connected to the ring in air secure fashion. Normally, the pivot axis of the cable coupling is not at the same height as the connection of the roof membrane or fabric to the compression ring in the vicinity of the cable, the cable coupling usually being spaced vertically a given distance below the membrane connection. As a consequence, a predetermined amount of slack may be provided in the membrane structure at the cable cross-over regions to accommodate the movement of the roof during inflation and deflation thereof. However, in an inflated mode, such slack accommodation introduces the undesirable structural trade-off of stress gradients both in the fabric as well as in the associated cable. Such trade-offs are seen to impose overall loading constraints upon the basic pressure criteria of the design analysis of the structure.